Number Systems Hierarchy

Visualize how N, W, Z, Q, and R are nested โ€” and where irrationals live.

About This Diagram

This interactive diagram shows the containment relationships among common number sets: Natural (โ„•), Whole (๐•Ž), Integers (โ„ค), Rational (โ„š), and Real (โ„) numbers. It also highlights Irrational numbers (๐•€) as real but not rational.

โ„• โŠ‚ ๐•Ž โŠ‚ โ„ค โŠ‚ โ„š โŠ‚ โ„
Natural (โ„•): 1, 2, 3, 15
Whole (๐•Ž): 0
Integers (โ„ค): -5, -12
Rational (โ„š): 1/2, 0.75, -2/3
Irrational (๐•€): ฯ€, โˆš2, e

Hover over a region to see its definition.